Solvability criterion for convolution equations on a half-strip
type: Item
instance of: scholarly article
title: Solvability criterion for convolution equations on a half-strip
zbMATH Open document ID: 1475.45005
author: V. M. Dil'nyj
published in: Complex Analysis and Operator Theory
publication date: 2021-08-17T00:00:00Z
review text: The author obtains a criterion for the solvability of the following homogeneous convolution equation defined on a halfstrip: \[ \int\limits_{\partial D_{\sigma}}f(\omega+\tau)g(\omega)d\omega=0, \; \tau\le 0, \; g\in L^2(-\infty,0). \] Here \(D_{\sigma}=\left\{z: \; \mathfrak{Re} z<0, \; |\mathfrak{Im} z|<\sigma \right\}, \; \sigma>0\). This is a generalization of the classical equation \[ \int\limits_{-\infty}^{0}f(u+\tau)g(u)du=0, \; \tau\le 0, \; g\in L^2(-\infty,0). \] The considered equation has direct applications in signal theory, in the study of cyclic functions and in information theory. The proof is based on a new decomposition property of weighted Hardy spaces.
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 30H10
zbMATH DE Number: 7382591
zbMATH Keywords: convolution equation
zbMATH Keywords: Hardy space
zbMATH Keywords: analytic continuation
zbMATH Keywords: spectral analysis
zbMATH Keywords: spectral synthesis
zbMATH Keywords: signal processing
reviewed by: Alexander N. Tynda
MaRDI profile type: Publication
full work available at URL: s11785-021-01120-8
OpenAlex ID: W3163541255
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DOI: 10.1007/S11785-021-01120-8
description: scientific article; zbMATH DE number 7382591